Observing and modeling nonlinear dynamics in an internal combustion engine

We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model's simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements.